SMALL-AMPLITUDE OSCILLATORY FORCING ON 2-LAYER PLANE CHANNEL FLOW

The effect of oscillatory forcing as a dynamic stabilization or destab ilization mechanism for two-layer plane Couette-Poiseuille flow at low Reynolds number is studied using numerical and asymptotic methods. Th e how is driven by the relative planar motion of the upper boundary an d a pressure gradient in the streamwise direction. Both driving forces are composed of a steady part and small-amplitude time-periodic fluct uations. An asymptotic expansion for the growth rates for small amplit udes is developed and the correction terms are quadratic in the amplit udes. The modulations to the steady flow can have either a stabilizing or destabilizing influence depending upon the conditions of flow. Com plete stabilization is possible for certain flows which are otherwise unstable owing to the viscosity stratification across the interface. T he combined pressure and velocity fluctuations can have an opposite ef fect on the flow stability to that induced by the separate time-period ic forcing mechanisms.